Inverse Kinematics

This entry discusses the rigging feature known as Inverse Kinematics (IK).  In Blender this is available when in Pose Mode, and can be found in the Tools [T] menu (as shown below).

When this is enabled, essentially, parent bones will automatically adjust to the movements of the most child bone.  In the image below, the lowest bone is being translated, and the parent bones are being bent accordingly.  Conversely, without Auto IK, you would have to rotated and translate each bone separately working from the parent down to the child.

The general rule for when to apply IK or not, is for limbs that bear weight or support the rest of the armature, IK should be used, for everything else use Forward Kinematics.